【发布时间】：2016-08-01 19:43:33
【问题描述】：
我正在尝试在 MS 的 Excel VBA 中实现快速傅立叶变换 (Radix-2)。我正在使用的代码从工作表的某个范围中提取数据，进行计算，然后将结果转储到相邻列中。我遇到的问题是 1）知道如何处理生成的 X[k] 数组，以及 2）将这些结果与 Excel 内置 FFT 的结果相匹配（它们目前不匹配）。代码如下所示。在此先感谢您的帮助。
Sub Enforce_DecimationInTime()
On Error GoTo ERROR_HANDLING
Dim SubName As String
SubName = "Enforce_DecimationInTime()"
Dim WS As Worksheet
Dim n As Long, v As Long, LR As Long, x As Long
Set WS = Worksheets("FFT")
LR = WS.Range("A" & Rows.Count).End(xlUp).Row
n = LR - 1
Do Until 2 ^ x <= n And 2 ^ (x + 1) > n 'locates largest power of 2 from size of input array
x = x + 1
Loop
n = n - (n - 2 ^ x) 'calculates n using the largest power of 2
If n + 1 <> WS.Range("A" & Rows.Count).End(xlUp).Row Then
WS.Range("A" & 2 ^ x + 2 & ":A" & LR).Delete xlUp 'deletes extra input data
End If
v = WorksheetFunction.Log(n, 2) 'calculates number of decimations necessary
Application.ScreenUpdating = False
For x = 1 To v
Call Called_Core.DecimationInTime(WS, n, 2 ^ x, x) 'calls decimation in time subroutine
Next x
Application.ScreenUpdating = True
Exit Sub
ERROR_HANDLING:
MsgBox "Error encountered in " & SubName & ": exiting subroutine." _
& vbNewLine _
& vbNewLine & "Error description: " & Err.Description _
& vbNewLine & "Error number: " & Err.Number, vbCritical, Title:="Error!"
End
End Sub
上面的子程序通过 For/Next 循环调用下面的子程序到 "v" 的计数。
Sub DecimationInTime(WS As Worksheet, n As Long, Factor As Integer, x As Long)
On Error GoTo ERROR_HANDLING
Dim SubName As String
SubName = "DecimationInTime()"
Dim f_1() As Single, f_2() As Single
Dim i As Long, m As Long, k As Long
Dim TFactor_N1 As String, TFactor_N2 As String, X_k() As String
Dim G_1() As Variant, G_2() As Variant
ReDim f_1(0 To n / Factor - 1) As Single
ReDim f_2(0 To n / Factor - 1) As Single
ReDim G_1(0 To n / 1 - 1) As Variant
ReDim G_2(0 To n / 1 - 1) As Variant
ReDim X_k(0 To n - 1) As String
TFactor_N1 = WorksheetFunction.Complex(0, -2 * WorksheetFunction.Pi / (n / 1)) 'twiddle factor for N
TFactor_N2 = WorksheetFunction.Complex(0, -2 * WorksheetFunction.Pi / (n / 2)) 'twiddle factor for N/2
For i = 0 To n / Factor - 1
f_1(i) = WS.Range("A" & 2 * i + 2).Value 'assign input data
f_2(i) = WS.Range("A" & 2 * i + 3).Value 'assign input data
Next i
WS.Cells(1, 1 + x).Value = "X[" & x & "]" 'labels X[k] column with k number
For k = 0 To n / 2 - 1
For m = 0 To n / Factor - 1
G_1(m) = WorksheetFunction.ImProduct(WorksheetFunction.ImPower(TFactor_N2, k * m), WorksheetFunction.Complex(f_1(m), 0)) 'defines G_1[m]
G_2(m) = WorksheetFunction.ImProduct(WorksheetFunction.ImPower(TFactor_N2, k * m), WorksheetFunction.Complex(f_2(m), 0)) 'defines G_2[m]
Next m
X_k(k) = WorksheetFunction.ImSum(WorksheetFunction.ImSum(G_1), WorksheetFunction.ImProduct(WorksheetFunction.ImSum(G_2), WorksheetFunction.ImPower(TFactor_N1, k))) 'defines X[k] for k
If k <= n / 2 Then X_k(k + n / 2) = WorksheetFunction.ImSum(WorksheetFunction.ImSum(G_1), WorksheetFunction.ImProduct(WorksheetFunction.ImSum(G_2), WorksheetFunction.ImPower(TFactor_N1, k), WorksheetFunction.Complex(-1, 0))) 'defines X[k] for k + n/2
WS.Cells(k + 2, 1 + x).Value = X_k(k)
WS.Cells(k + 2 + n / 2, 1 + x).Value = X_k(k + n / 2)
Next k
Exit Sub
ERROR_HANDLING:
MsgBox "Error encountered in " & SubName & ": exiting subroutine." _
& vbNewLine _
& vbNewLine & "Error description: " & Err.Description _
& vbNewLine & "Error number: " & Err.Number, vbCritical, Title:="Error!"
End
End Sub
【问题讨论】：
-
由于内置的 FFT 可能是用 C 实现的，它至少比 VBA 中的任何东西都快一个数量级。有什么理由不想使用它？可以从 VBA 调用它。看到这个：cpearson.com/excel/atp.htm
-
是的，我知道与许多其他语言相比，VBA 的运行速度会非常慢。内置 FFT 的输入数组限制为 4096，我想通过 FFT 运行更大的数组（尽管时间显着增加）。另外，我更愿意学习实际的算法，而不是让程序为我完成工作。
-
对我来说很有意义——我只是认为你有可能不知道你可以直接在 VBA 中使用它。自己实现这样的算法绝对是一种学习体验。从更实际的角度来看——你也许可以看看这个：newtonexcelbach.wordpress.com/2015/05/05/xlscipy-1-01（即使你不走那条路，包含这篇文章的博客对于任何想要进行核心科学计算的人来说都是一本好书在 Excel 中）
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谢谢，我一定会完成的。
标签： algorithm excel signal-processing fft vba